The objective of this Faculty Early Career Development (CAREER) Program award is to devise and study algorithms for large-scale random systems where direct computation is infeasible despite today's ever-increasing availability and affordability of computing resources. This project focuses on three stylized settings: (1) The project aims to introduce new Monte Carlo algorithms for rare event simulation and to show how these are widely applicable, including in cases where no efficient algorithms have currently been found. (2) The project aims to devise and assess the performance of resource allocation algorithms in large-scale stochastic networks such as computer clouds, specifically to increase the understanding of how allocation algorithms affect quality of service. This requires developing a novel methodology for stochastic networks and their scaling properties. (3) The project aims to study a class of algorithms for sampling from high-dimensional sets, where the specific focus lies on algorithms that exploit boundaries.
If successful, the results of this research will lead to effective algorithms for large-scale random systems, along with accompanying qualitative insights and mathematical performance analysis. The results will for instance help in computing probabilities of rare but significant events. They will also help in understanding and managing large-scale service systems. Furthermore, they will aid in improving internal efficiencies in large-scale computer systems, which becomes ever more important in the face of rising energy costs and associated environmental impact.
